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CRC校验

程序员文章站 2022-05-11 14:05:25
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一、下面是一个例子:

假定有待校验数据A = 1101,校验多项式B = 0000 0111,当前CRC校验值 CRC = 1011 1001,
步骤0:CRC = 1011 1001 首先与数据A左移4位后异或得到新CRC1 = 10111001^1101 0000 = 0110 1001;
步骤1:CRC1 首位为0, CRC1左移1位得 CRC2 = 1101
步骤2:CRC2首位为1, CRC2左移1位得 CRC3 = 1010 0100, 然后CRC3与校验多项式B异或得
CRC4 = 1010 0100 ^ 0000 0111= 1010 0011;
步骤3:CRC4首位为1,CRC4左移1位得CRC5 = 0100 0110, 然后CRC5与校验多项式B异或得 CRC6 = 0100 0110^ 0000 0111 = 0100 0001;
步骤4:CRC6首位为0, CRC6左移1位得CRC7 = 1000 0010;
至此,4位宽度计算完成。从以上过程可以看出,步骤1到步骤4的执行过程与步骤0所得的结果CRC1的高4位非常相关,
该高4位取值直接决定了步骤1到步骤4的运行结果; 进一步将CRC1划分为CRC1 = (0110 0000)^(00001001); 则结果就可以写成如下:C = (0110 0000)^(00001001)^(一系列校验多项式因CRC1高4位取值变化后的多项式)
备注1:步骤0-步骤4中的CRC值左移操作可以认为是CRC值不变,校验多项式随CRC1高4位取值不同进行变换。

因此,又可以根据CRC1的高4位取值与校验多项式预先生成一张2^4的码表,在实际计算的时候直接取CRC1
以预先计算出2^4,2^8个码值,常用是按照字节计算,则预先准备好2^8个码值。码值的位数则随使用的CRC校验宽度变化。

从CRC4的比较简单的检验过程中我们可以推断出CRC8和CRC16的校验过程是怎么样的。

二、CRC8,CRC16,CRC32如何选择:

根据所传输数据的多少,一般数据越多,CRC-m的m越大。

三、CRC校验代码实现:

 1. 直接按位运算(适用于对速度要求不高的场合):

(1) 设置CRC寄存器,并给其赋值为“余数初始值”。

(2) 将数据的第一个8-bit字符与CRC寄存器进行异或,并把结果存入CRC寄存器。

(3) CRC寄存器向右移一位,MSB补零,移出并检查LSB。

(4) 如果LSB为0,重复第三步;若LSB为1,CRC寄存器与0x31相异或。

(5) 重复第3与第4步直到8次移位全部完成。此时一个8-bit数据处理完毕。

(6) 重复第2至第5步直到所有数据全部处理完成。

(7) 最终CRC寄存器的内容与“结果异或值”进行或非操作后即为CRC值。

#include<stdio.h>

#define POLY        0x1021
/**
* Calculating CRC-16 in 'C'
* @para addr, start of data
* @para num, length of data
* @para crc, incoming CRC
*/
int crc16(unsigned char *addr, int num, int crc)
{
    int i;
    for (; num > 0; num--)              /* Step through bytes in memory */
    {
        crc = crc ^ (*addr++ << 8);     /* Fetch byte from memory, XOR into CRC top byte*/
        for (i = 0; i < 8; i++)             /* Prepare to rotate 8 bits */
        {
            if (crc & 0x8000)            /* b15 is set... */
                crc = (crc << 1) ^ POLY;    /* rotate and XOR with polynomic */
            else                          /* b15 is clear... */
                crc <<= 1;                  /* just rotate */
        }                             /* Loop for 8 bits */
        crc &= 0xFFFF;                  /* Ensure CRC remains 16-bit value */
    }                               /* Loop until num=0 */
    return(crc);                    /* Return updated CRC */
}

void main()
{
    unsigned char data1[] = { '1', '2', '3', '4', '5', '6', '7', '8', '9' };
    unsigned char data2[] = { '5', '6', '7', '8', '9' };
    unsigned short c1, c2;
    c1 = crc16(data1, 9, 0xffff);
    c2 = crc16(data1, 4, 0xffff);
    c2 = crc16(data2, 5, c2);
    printf("%04x\n", c1);
    printf("%04x\n", c2);

}
最后得到的C1和C2都为29b1

其中里面那个除数(多项式)也就是POLY的取值是:
经过专家验证的,一般CRC8为0x31,也就是X8+X5+X4+X0(最高次方一定为1);
其他的在下面表中:

CRC校验

2. 查表法(可以提高计算的效率):
uint16_t       CRC_INIT        = 0xffff;
const uint16_t wCRC_Table[256] = {
  0x0000, 0x1189, 0x2312, 0x329b, 0x4624, 0x57ad, 0x6536, 0x74bf,
  0x8c48, 0x9dc1, 0xaf5a, 0xbed3, 0xca6c, 0xdbe5, 0xe97e, 0xf8f7,
  0x1081, 0x0108, 0x3393, 0x221a, 0x56a5, 0x472c, 0x75b7, 0x643e,
  0x9cc9, 0x8d40, 0xbfdb, 0xae52, 0xdaed, 0xcb64, 0xf9ff, 0xe876,
  0x2102, 0x308b, 0x0210, 0x1399, 0x6726, 0x76af, 0x4434, 0x55bd,
  0xad4a, 0xbcc3, 0x8e58, 0x9fd1, 0xeb6e, 0xfae7, 0xc87c, 0xd9f5,
  0x3183, 0x200a, 0x1291, 0x0318, 0x77a7, 0x662e, 0x54b5, 0x453c,
  0xbdcb, 0xac42, 0x9ed9, 0x8f50, 0xfbef, 0xea66, 0xd8fd, 0xc974,
  0x4204, 0x538d, 0x6116, 0x709f, 0x0420, 0x15a9, 0x2732, 0x36bb,
  0xce4c, 0xdfc5, 0xed5e, 0xfcd7, 0x8868, 0x99e1, 0xab7a, 0xbaf3,
  0x5285, 0x430c, 0x7197, 0x601e, 0x14a1, 0x0528, 0x37b3, 0x263a,
  0xdecd, 0xcf44, 0xfddf, 0xec56, 0x98e9, 0x8960, 0xbbfb, 0xaa72,
  0x6306, 0x728f, 0x4014, 0x519d, 0x2522, 0x34ab, 0x0630, 0x17b9,
  0xef4e, 0xfec7, 0xcc5c, 0xddd5, 0xa96a, 0xb8e3, 0x8a78, 0x9bf1,
  0x7387, 0x620e, 0x5095, 0x411c, 0x35a3, 0x242a, 0x16b1, 0x0738,
  0xffcf, 0xee46, 0xdcdd, 0xcd54, 0xb9eb, 0xa862, 0x9af9, 0x8b70,
  0x8408, 0x9581, 0xa71a, 0xb693, 0xc22c, 0xd3a5, 0xe13e, 0xf0b7,
  0x0840, 0x19c9, 0x2b52, 0x3adb, 0x4e64, 0x5fed, 0x6d76, 0x7cff,
  0x9489, 0x8500, 0xb79b, 0xa612, 0xd2ad, 0xc324, 0xf1bf, 0xe036,
  0x18c1, 0x0948, 0x3bd3, 0x2a5a, 0x5ee5, 0x4f6c, 0x7df7, 0x6c7e,
  0xa50a, 0xb483, 0x8618, 0x9791, 0xe32e, 0xf2a7, 0xc03c, 0xd1b5,
  0x2942, 0x38cb, 0x0a50, 0x1bd9, 0x6f66, 0x7eef, 0x4c74, 0x5dfd,
  0xb58b, 0xa402, 0x9699, 0x8710, 0xf3af, 0xe226, 0xd0bd, 0xc134,
  0x39c3, 0x284a, 0x1ad1, 0x0b58, 0x7fe7, 0x6e6e, 0x5cf5, 0x4d7c,
  0xc60c, 0xd785, 0xe51e, 0xf497, 0x8028, 0x91a1, 0xa33a, 0xb2b3,
  0x4a44, 0x5bcd, 0x6956, 0x78df, 0x0c60, 0x1de9, 0x2f72, 0x3efb,
  0xd68d, 0xc704, 0xf59f, 0xe416, 0x90a9, 0x8120, 0xb3bb, 0xa232,
  0x5ac5, 0x4b4c, 0x79d7, 0x685e, 0x1ce1, 0x0d68, 0x3ff3, 0x2e7a,
  0xe70e, 0xf687, 0xc41c, 0xd595, 0xa12a, 0xb0a3, 0x8238, 0x93b1,
  0x6b46, 0x7acf, 0x4854, 0x59dd, 0x2d62, 0x3ceb, 0x0e70, 0x1ff9,
  0xf78f, 0xe606, 0xd49d, 0xc514, 0xb1ab, 0xa022, 0x92b9, 0x8330,
  0x7bc7, 0x6a4e, 0x58d5, 0x495c, 0x3de3, 0x2c6a, 0x1ef1, 0x0f78
};
uint16_t get_crc16_check_sum(uint8_t* pchMessage, uint32_t dwLength, uint16_t wCRC)
{//可以得到CRC16的校验结果
  uint8_t chData;
  if (pchMessage == NULL)
  {
    return 0xFFFF;
  }
  while (dwLength--)
  {
    chData = *pchMessage++;
    (wCRC) = ((uint16_t)(wCRC) >> 8) ^ wCRC_Table[((uint16_t)(wCRC) ^ (uint16_t)(chData)) & 0x00ff];
  }
  return wCRC;
}
//上面是RM给的官方例程校验的方法,官方采用的方法是反向算法
#include<crc.h>
//下面是根据自己的理解和官方的程序自己写的
/*******************
CRC8的多项式:g(x) = X8+X5+X4+X0   0x31
********************/
const u8 CRC8_INIT     = 0xff;
const u8 CRC8_Table[256] = {
  0x00, 0x5e, 0xbc, 0xe2, 0x61, 0x3f, 0xdd, 0x83, 0xc2, 0x9c, 0x7e, 0x20, 0xa3, 0xfd, 0x1f, 0x41,
  0x9d, 0xc3, 0x21, 0x7f, 0xfc, 0xa2, 0x40, 0x1e, 0x5f, 0x01, 0xe3, 0xbd, 0x3e, 0x60, 0x82, 0xdc,
  0x23, 0x7d, 0x9f, 0xc1, 0x42, 0x1c, 0xfe, 0xa0, 0xe1, 0xbf, 0x5d, 0x03, 0x80, 0xde, 0x3c, 0x62,
  0xbe, 0xe0, 0x02, 0x5c, 0xdf, 0x81, 0x63, 0x3d, 0x7c, 0x22, 0xc0, 0x9e, 0x1d, 0x43, 0xa1, 0xff,
  0x46, 0x18, 0xfa, 0xa4, 0x27, 0x79, 0x9b, 0xc5, 0x84, 0xda, 0x38, 0x66, 0xe5, 0xbb, 0x59, 0x07,
  0xdb, 0x85, 0x67, 0x39, 0xba, 0xe4, 0x06, 0x58, 0x19, 0x47, 0xa5, 0xfb, 0x78, 0x26, 0xc4, 0x9a,
  0x65, 0x3b, 0xd9, 0x87, 0x04, 0x5a, 0xb8, 0xe6, 0xa7, 0xf9, 0x1b, 0x45, 0xc6, 0x98, 0x7a, 0x24,
  0xf8, 0xa6, 0x44, 0x1a, 0x99, 0xc7, 0x25, 0x7b, 0x3a, 0x64, 0x86, 0xd8, 0x5b, 0x05, 0xe7, 0xb9,
  0x8c, 0xd2, 0x30, 0x6e, 0xed, 0xb3, 0x51, 0x0f, 0x4e, 0x10, 0xf2, 0xac, 0x2f, 0x71, 0x93, 0xcd,
  0x11, 0x4f, 0xad, 0xf3, 0x70, 0x2e, 0xcc, 0x92, 0xd3, 0x8d, 0x6f, 0x31, 0xb2, 0xec, 0x0e, 0x50,
  0xaf, 0xf1, 0x13, 0x4d, 0xce, 0x90, 0x72, 0x2c, 0x6d, 0x33, 0xd1, 0x8f, 0x0c, 0x52, 0xb0, 0xee,
  0x32, 0x6c, 0x8e, 0xd0, 0x53, 0x0d, 0xef, 0xb1, 0xf0, 0xae, 0x4c, 0x12, 0x91, 0xcf, 0x2d, 0x73,
  0xca, 0x94, 0x76, 0x28, 0xab, 0xf5, 0x17, 0x49, 0x08, 0x56, 0xb4, 0xea, 0x69, 0x37, 0xd5, 0x8b,
  0x57, 0x09, 0xeb, 0xb5, 0x36, 0x68, 0x8a, 0xd4, 0x95, 0xcb, 0x29, 0x77, 0xf4, 0xaa, 0x48, 0x16,
  0xe9, 0xb7, 0x55, 0x0b, 0x88, 0xd6, 0x34, 0x6a, 0x2b, 0x75, 0x97, 0xc9, 0x4a, 0x14, 0xf6, 0xa8,
  0x74, 0x2a, 0xc8, 0x96, 0x15, 0x4b, 0xa9, 0xf7, 0xb6, 0xe8, 0x0a, 0x54, 0xd7, 0x89, 0x6b, 0x35,
};
/*******************
CRC16的多项式:g(x) = x16+x12+x5+x0  0x1021
********************/

const u16 CRC16_INIT        = 0xffff;
const u16 CRC16_Table[256] = {
  0x0000, 0x1189, 0x2312, 0x329b, 0x4624, 0x57ad, 0x6536, 0x74bf,
  0x8c48, 0x9dc1, 0xaf5a, 0xbed3, 0xca6c, 0xdbe5, 0xe97e, 0xf8f7,
  0x1081, 0x0108, 0x3393, 0x221a, 0x56a5, 0x472c, 0x75b7, 0x643e,
  0x9cc9, 0x8d40, 0xbfdb, 0xae52, 0xdaed, 0xcb64, 0xf9ff, 0xe876,
  0x2102, 0x308b, 0x0210, 0x1399, 0x6726, 0x76af, 0x4434, 0x55bd,
  0xad4a, 0xbcc3, 0x8e58, 0x9fd1, 0xeb6e, 0xfae7, 0xc87c, 0xd9f5,
  0x3183, 0x200a, 0x1291, 0x0318, 0x77a7, 0x662e, 0x54b5, 0x453c,
  0xbdcb, 0xac42, 0x9ed9, 0x8f50, 0xfbef, 0xea66, 0xd8fd, 0xc974,
  0x4204, 0x538d, 0x6116, 0x709f, 0x0420, 0x15a9, 0x2732, 0x36bb,
  0xce4c, 0xdfc5, 0xed5e, 0xfcd7, 0x8868, 0x99e1, 0xab7a, 0xbaf3,
  0x5285, 0x430c, 0x7197, 0x601e, 0x14a1, 0x0528, 0x37b3, 0x263a,
  0xdecd, 0xcf44, 0xfddf, 0xec56, 0x98e9, 0x8960, 0xbbfb, 0xaa72,
  0x6306, 0x728f, 0x4014, 0x519d, 0x2522, 0x34ab, 0x0630, 0x17b9,
  0xef4e, 0xfec7, 0xcc5c, 0xddd5, 0xa96a, 0xb8e3, 0x8a78, 0x9bf1,
  0x7387, 0x620e, 0x5095, 0x411c, 0x35a3, 0x242a, 0x16b1, 0x0738,
  0xffcf, 0xee46, 0xdcdd, 0xcd54, 0xb9eb, 0xa862, 0x9af9, 0x8b70,
  0x8408, 0x9581, 0xa71a, 0xb693, 0xc22c, 0xd3a5, 0xe13e, 0xf0b7,
  0x0840, 0x19c9, 0x2b52, 0x3adb, 0x4e64, 0x5fed, 0x6d76, 0x7cff,
  0x9489, 0x8500, 0xb79b, 0xa612, 0xd2ad, 0xc324, 0xf1bf, 0xe036,
  0x18c1, 0x0948, 0x3bd3, 0x2a5a, 0x5ee5, 0x4f6c, 0x7df7, 0x6c7e,
  0xa50a, 0xb483, 0x8618, 0x9791, 0xe32e, 0xf2a7, 0xc03c, 0xd1b5,
  0x2942, 0x38cb, 0x0a50, 0x1bd9, 0x6f66, 0x7eef, 0x4c74, 0x5dfd,
  0xb58b, 0xa402, 0x9699, 0x8710, 0xf3af, 0xe226, 0xd0bd, 0xc134,
  0x39c3, 0x284a, 0x1ad1, 0x0b58, 0x7fe7, 0x6e6e, 0x5cf5, 0x4d7c,
  0xc60c, 0xd785, 0xe51e, 0xf497, 0x8028, 0x91a1, 0xa33a, 0xb2b3,
  0x4a44, 0x5bcd, 0x6956, 0x78df, 0x0c60, 0x1de9, 0x2f72, 0x3efb,
  0xd68d, 0xc704, 0xf59f, 0xe416, 0x90a9, 0x8120, 0xb3bb, 0xa232,
  0x5ac5, 0x4b4c, 0x79d7, 0x685e, 0x1ce1, 0x0d68, 0x3ff3, 0x2e7a,
  0xe70e, 0xf687, 0xc41c, 0xd595, 0xa12a, 0xb0a3, 0x8238, 0x93b1,
  0x6b46, 0x7acf, 0x4854, 0x59dd, 0x2d62, 0x3ceb, 0x0e70, 0x1ff9,
  0xf78f, 0xe606, 0xd49d, 0xc514, 0xb1ab, 0xa022, 0x92b9, 0x8330,
  0x7bc7, 0x6a4e, 0x58d5, 0x495c, 0x3de3, 0x2c6a, 0x1ef1, 0x0f78
};
/*
函数名称:Check_CRC8
入口参数:data:传入数据的地址
                 length:数据长度
                 cnt_init:校验初始化
返回参数:CRC8位校验的返回值
*/


u8 Check_CRC8(u8 *data, u16 length,u8 cnt_init)
{
    u8 CRC_Res=cnt_init;
    while(length--)
    {
        CRC_Res=CRC8_Table[CRC_Res^(*data++)];
    }
    return CRC_Res;
}



/*
函数名称:Check_CRC16
入口参数:data:传入数据的地址
                 length:数据长度
                 cnt_init:校验初始化
返回参数:CRC16位校验的返回值
*/

u16 Check_CRC16(u8 *data,u16 length,u16 cnt_init)
{
    u16 CRC_Res=cnt_init;   
    while(length--)
    {
        CRC_Res=((u16)(CRC_Res>>8))^CRC16_Table[((u16)(CRC_Res)^(u16)(*data++))&0x00ff];
    }
    return (CRC_Res);
}





//下面是数据传输的过程,这次传输只是用了串口接受中断和空闲中断,后面会加上DMA传输完成中断

extern u16 CRC16_INIT;
extern u8  CRC8_INIT;
void USART1_IRQHandler(void)
{
    u8 data=data;
    u8 i;
    if(USART_GetITStatus(USART1, USART_IT_RXNE))
    {
        RX_Buffer[RX_Cnt++]=USART_ReceiveData(USART1);
    }
    else if(USART_GetITStatus(USART1,USART_IT_IDLE))
    {
        data=USART1->SR;
        data=USART1->DR;
        ReceiveState=1;//标志一帧数据接受完成
    }

    if(ReceiveState)
    {
        u8 CRC8=0;
        u16 CRC16=0;
        i=0;
        ReceiveState=0;
        CRC16=Check_CRC16(RX_Buffer,RX_Cnt,CRC16_INIT); 
        CRC8=Check_CRC8(RX_Buffer,RX_Cnt,CRC8_INIT);            
        USART_SendData(USART1,(u8)RX_Cnt);
        while(!USART_GetFlagStatus(USART1,USART_FLAG_TC));//接受完成标志
        while(RX_Cnt--)
        {
            USART_SendData(USART1,RX_Buffer[i++]);
            while(!USART_GetFlagStatus(USART1,USART_FLAG_TC));//接受完成标志
        }   
        USART_SendData(USART1,CRC16>>8);
        while(!USART_GetFlagStatus(USART1,USART_FLAG_TC));//接受完成标志
        USART_SendData(USART1,(u8)CRC16);
        while(!USART_GetFlagStatus(USART1,USART_FLAG_TC));//接受完成标志

        USART_SendData(USART1,(u8)CRC8);
        while(!USART_GetFlagStatus(USART1,USART_FLAG_TC));//接受完成标志
        RX_Cnt=0;
    }
}


/*
然后我简单校验了一下0x31 0x32 0x33 0x34 0x35 0x36 0x37 0x38 0x39也就是123456789对应的ASCII
码,最后对应CRC16的值为0x6f91 CRC8的值为0x0b
*/
相关标签: RM